An asteroid in orbit about the sun has a linear speed of 4km/s when at a distance of closest approach d from the sun. What is its linear speed when it is at its greatest distance from the sun a distance 2d? a. 1km/s b. 2km/s c. 8km/s d. 16km/s

Found a large planet the size of Jupiter orbiting a star.  The distance of the planet is 1/9 times the distance between Mercury and the sun.  The planet takes 3.09 days to make one orbit (assuming circular).  How fast is the planet moving?  (Knowing G = 6.67 × 10^-11 N m²/kg², distance of Mercury from the sun = 5.79 x 1010 m) a.  131 km/s b.  141 km/s c.  151 km/s d.  161 km/s e.  171 km/s

4. We are planning a human exploration mission to Mars. We will first place our spacecraft into a circular around Mars and then send down a lander. a) If we want the spacecraft to orbit at an altitude of 170 km above the Martian surface, what will the velocity and orbital period of the spacecraft? b) When we land astronauts on the surface of Mars, what acceleration due to gravity in terms of g's (i.e. as a fraction of the Earth's gravitational acceleration) will the astronauts experience? You are permitted to use an online resource (e.g. Google) to find the necessary information about Mars that you might need in solving this problem.